Problem: The value of $\sqrt{57}$ lies between which two consecutive integers ? Integers that appear in order when counting, for example 2 and 3.
Explanation: Consider the perfect squares near $57$ . [ What are perfect squares? Perfect squares are integers which can be obtained by squaring an integer. The first 13 perfect squares are: $ 1,4,9,16,25,36,49,64,81,100,121,144,169$ $49$ is the nearest perfect square less than $57$ $64$ is the nearest perfect square more than $57$ So, we know $49 < 57 < 64$ So, $\sqrt{49} < \sqrt{57} < \sqrt{64}$ So $\sqrt{57}$ is between $7$ and $8$.